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A deep learning method for computing mean exit time excited by weak Gaussian noise

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Abstract

Exit events induced by noise from the attracting domain containing a stable fixed point are ubiquitous phenomena in physical systems, wherein mean exit time is an important quantity which has been widely used in engineering, physical, chemical and biological fields. In this work, we devise a deep learning method to compute the mean exit time for dynamical systems excited by weak Gaussian noise. More specifically, we first derive a complete group of ordinary differential equations governing the most probable path, the quasipotential, and the prefactor along the path via WKB approximation. Then a neural network architechture is proposed to solve it in terms of automatic differentiation. The results of numerical experiments show the effectiveness and accuracy of the algorithm and imply its potential applications to discover the mechanisms of rare events triggered by random fluctuations in practical models.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Funding

The authors acknowledge support from the National Natural Science Foundation of China (Grant Nos. 12302035, 62073166, 62221004), the Natural Science Foundation of Jiangsu Province (Grant No. BK20220917), the Key Laboratory of Jiangsu Province, the Shandong Provincial Natural Science Foundation under Grant ZR2021ZD13, and the Project on the Technological Leading Talent Teams Led by Frontiers Science Center for Complex Equipment System Dynamics (FSCCESD220401).

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, 200 Xiaolingwei Street, Nanjing, 210094, China

    Yang Li & Shengyuan Xu

  2. State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing, 210016, China

    Feng Zhao & Xianbin Liu

  3. Departments of Applied Mathematics & Physics, Illinois Institute of Technology, Chicago, IL, 60616, USA

    Jinqiao Duan

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  1. Yang Li
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  2. Feng Zhao
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  3. Shengyuan Xu
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  4. Jinqiao Duan
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  5. Xianbin Liu
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Correspondence to Shengyuan Xu.

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Li, Y., Zhao, F., Xu, S. et al. A deep learning method for computing mean exit time excited by weak Gaussian noise. Nonlinear Dyn 112, 5541–5554 (2024). https://doi.org/10.1007/s11071-024-09280-w

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